Measuring nonstabilizerness via multifractal flatness

Understand

Universal quantum computing requires nonstabilizer (magic) quantum states.

• Quantifying the nonstabilizerness and relating it to other quantum resources is vital for characterizing the complexity of quantum many-body systems.
• In this work, we prove that a quantum state is a stabilizer if and only if all states belonging to its Clifford orbit have a flat probability distribution on the computational basis.
• This implies, in particular, that multifractal states are nonstabilizers.